Presentation
SIGN IN TO VIEW THIS PRESENTATION Sign In
A Practical Quantum Solver for Multidimensional Partial Differential Equations
DescriptionQuantum computing has the potential to transform computational problem-solving by leveraging quantum mechanical principles of superposition and entanglement. This capability is particularly important for the numerical solution of complex and/or multidimensional partial-differential-equations (PDEs). The existing quantum PDE solvers, particularly those based on variational-quantum-algorithms (VQAs) suffer from limitations such as low accuracy, high execution times, and low scalability. In this work, we propose an efficient and scalable algorithm for solving multidimensional PDEs. We present two variants of our algorithm: the first leverages finite-difference-method (FDM), classical-to-quantum (C2Q) encoding, and numerical instantiation, while the second employs FDM, C2Q, and column-by-column decomposition (CCD). We have validated our proposed algorithm by solving several practically useful PDEs such as Poisson, heat, Black-Scholes, and Navier-Stokes equations. Our results demonstrate higher accuracy, higher scalability, and faster execution times compared to VQA-based solvers on noise-free and noisy quantum simulators from IBM and achieved promising results on real quantum hardware.
Author/Presenters
